Stability Analysis Of Continuous Runge - Kutta Method For Solving Generalized Delay Differential Algebraic Systems

Delay differential-algebraic equations(DDAEs) and Neutral delay differential-algebraic equa-tions(NDDAEs) arises in a wide variety of scientific and engineering applications, including cir-cuit analysis, optimal control, real-time simulation, chemical process simulation computer-aideddesign and management system. the stability of numerical methods for DDAEs and NDDAEshave been very intensively studied. however, for GDDAEs and GNDDAEs, in our search the vec-tor of the unknown component contains different time delay. So its stability analysis is relativelycomplex; In the paper, numerical experiment explains the influences of the different time delayfor stability.In this paper, we investigate the asymptotic stability of analytical and numerical solutions ofGDDAEs and GNDDAEs. First, by researching the roots of corresponding characteristic equation,we give and prove a sufficient condition under which GDDAEs and GNDDAEs are asymptoticalstable.then, we discuss the asymptotic stability of ontinuous Runge-Kutta methods when they areapplied to asymptotical stable GDDAEs and GNDDAEs. At last, some numerical experiments arecarried out in order to demonstrate the conclusions.